[ieee 2012 ieee international conference on control system, computing and engineering (iccsce) -...

Hyperspectral Band Referencing Based On Correlation Structure

Ayman Mahmoud Ahmed Egyptian Space Program

National Authorty for Remote Sensing and Space science

Cairo, Egypt [email protected]

Salwa ElRamly

Department of Electronics and Communication Engineering

Ain-Shams University Cairo, Egypt

[email protected]

Mohamed El. Sharkawy

E-JUST—Egypt-Japan University of science and technology, New Borg

El Arab, Alexandria, Egypt [email protected]

Abstract—Hyperspectral imaging has been widely studied in many applications; notably in climate changes, vegetation, and desert studies. However, such kind of imaging brings a huge amount of data, which requires transmission, processing, and storage resources for both airborne and space borne imaging. Compression of hyperspectral data cubes is an effective solution for these problems. Lossless compression of the hyperspectral data usually results in low compression ratio, which may not meet the available resources; on the other hand, lossy compression may give the desired ratio, but with a significant degradation effect on object identification performance of the hyperspectral data. Moreover, most hyperspectral data compression techniques exploits the similarities in spectral dimensions; which requires bands reordering or regrouping, to make use of the spectral redundancy. In this paper, we analyze the spectral cross correlation between bands for AVIRIS and Hyperion hyperspectral data; spectral cross correlation matrix is calculated, assessing the strength of the spectral matrix, and finally, we propose new technique to find highly correlated groups of bands in the hyperspectral data cube based on "inter band correlation square" referencing.

Keywords-hyperspectral imaging; band reordering; edge detection; spectral correlation matrix component

I. INTRODUCTION

Hyperspectral data contains a huge amount of spectral data distinctive in spectral resolution, which allows identification of each pixel, based on its spectral signature. On the other hand; this amount of data increases as spectral bands increase, usually satellite instrument that measures earth's illumination at specified spectral band, has more dynamic range than visual images; typically ranges from 10 up to 16 bits per pixel per band; additionally, considering the swath width of the satellite imagery; hyperspectral imaging session of satellite may contain tremendous amount of digital data to be transmitted to ground station [1]; this limits the imaging session and spatial resolution. Many researches have been conducted to efficiently "carefully" compress this amount of data without losing the main advantage of hyperspectral imaging which is spectral resolution; two known compression approaches are usually investigated, lossy and lossless techniques; lossless

compression is perfect for compression data and keeping the original information without distortion and in the same time allow further processing of the image to identify earth's objects accurately; unfortunately this approach of compassion gives compression ratio ranges from 1 up to 3 [2], [3]; that means the compressed data will have smaller volume down to 3 times less the original one; this, in practical situations, is not sufficient, and compressed data still represent a significant issue for onboard satellite designer for transmission and storage [4]. On the other hand; lossy compression approach gives a great compression ratio, which may go to 40 times; this ratio, is achieved scarifying the low distortion rate; that means more losses will appear on the reconstructed data; this losses can and will affect the process of earth's object identification process [4]. Another approach of compression is known as near lossless; this approach achieves relatively higher compression ratio than achieved by lossless approach and smaller distortion less than resulted from lossy compression approach; that is controlled by losses threshold. Meanwhile researches are continuing to find optimum solution that can fit onboard satellites [5]; most researches goes around exploitation of either spectral or spatial redundancy of hyperspectral data or both of them; spatial redundancy results from the fact that imaging certain territory will have similarity in spatial dimensions; these characteristics are exhaustively investigated during last decades; and as a result we have discrete cosine transformation and wavelet transformation [3]; it exploits the spatial redundancy in the images in different ways of implementation either in ground image processing software or onboard satellite instrumentations. On the other hand; spectral redundancy is relatively a new dimension in hyperspectral imaging; many researches are trying to investigate the best way to deal with this redundancy [7], [8] and optimum techniques to exploit it; these facts lead to another activity of investigation and analysis of spectral structure of hyperspectral data [9], [10], this analysis will put the main outlines and answers on how to best utilize inter-band spectral correlation in hyperspectral data.

2012 IEEE International Conference on Control System, Computing and Engineering, 23 - 25 Nov. 2012, Penang, Malaysia

978-1-4673-3143-2/12/$31.00 ©2012 IEEE 5

This paper is organized as follow; first section discusses the origin of the topic, followed by explaining similarity measurement and cross correlation compared with other similarity measuring techniques in second section; the term spectral cross correlation matrix (SCM) is defined in third section; estimation of spectral correlation matrix for hyperspectral data samples and analysis of the matrices are introduced in section four and five, respectively; section six introduces a new term of spectral correlation square for bands referencing, and finally we conclude this research and recommend results usage in last section.

II. INTER-BAND SPECTRAL CROSS CORRELATION AND SIMILARITY MEASUREMENT

Hyperspectral data can be viewed as a "Data-Cube"; this data cube has two spatial dimensions and one spectral dimension, spectral dimension represent the captured image in different spectral bands, usually successive and typically around 250 bands. Spectral redundancy is based on the similarity between bands and each other’s; these similarity can be measured by spectral cross correlation [11], Conditional entropy, mutual information, Euclidian Distance, Maximum Absolute Distance, and Centered Euclidian Distance; these measures are well studied by researchers and compared to determine which one is best fit for reordering the bands for prediction based compression techniques; correlation is found to be the best for similarity measurement [8], [12], [13]; this fact is a good point to start the analysis of spectral structure of the hyperspectral data cube. Correlation between spectral bands is named "spectral correlation" as it represents the correlation between two identical images in different spectral domains. The imaged piece of land by hyperspectral instrument is treated as unknown object, since the main objective of the satellite imagery is to provide data about these objects. The dependencies between bands should be reflectance of the material spectral response collected by imager, which is unknown; this may appear to be random dependencies, but the average correlation between bands is the main measuring criteria of similarity, which is dependent on average material spectral response within the single band. Cross correlation is usually a standard measure of degree of similarity between tow images (matrices); some techniques of cross correlation estimation was used to investigate the hyperspectral inter-band correlation; this process is time consuming and requires extensive computational power. Cross correlation mainly depends on covariance calculation between the two bands; while normalized cross correlation uses variance of each band as divisor to remove values dependency on the variation of both brightness and contrast of the image. Selection of estimation technique should be based on deterministic criteria; such as simplicity, speed, minimum resources of memory and computational power. Fast normalized cross correlation [14], [15] is a very good technique for calculating

the similarity between two images; it is fast and calculate how much similarity two images are independent of their individual brightness and contrast.

III. SPECTRAL CROSS CORRELATION MATRIX

Using fast normalized cross correlation techniques, correlation between all hyperspectral bands in the data cube is estimated; for band i, correlation value is estimated with all other bands in the data cube j; using the Eq. (1). Data cube is estimated; for band i, correlation value is estimated with all other bands in the data cube j; using the Eq. (1).

∑ −×∑ −

∑ −×−

=

yxDyxD

yxDyxD

yxDyxDDyxD

jiNCCjjii

jjii

,2)),((

,2)),((

,)]),(()),([(

),(

(1)

Where: NCC(i,j): Normalized cross correlation between bands i. and j, iD (x,y): intensity of pixel, (x, y) pixel indices within

one band, iD : mean of pixel intensity values of band i. This function is implemented in fast, optimized way in Matlab image processing tool box [16], based on "Fast Normalized Cross-Correlation" [14]. Estimation of the correlation value for the entire data cubes, is time consuming and needs powerful machine; we propose to use wavelet transform first to minimize size of each band to the half in each axes; which results in band size quarter of the original one; at the same time resulted spectral correlation matrix will still almost the same, Fig. 1.; while the correlation between these two matrices is 0.9137; this value is accepted, since we will be interesting to find some region within the matrix itself, this will be more clear in the analysis of the data. Estimating the inter-band cross correlation matrix for each hyperspectral data cube as stated in section 3; the resulted spectral correlation matrix for ten hyperspectral data samples, from both airborne and space borne instruments [17], [18], are illustrated in Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, and Fig. 9. As initially observed some data cubes have strong average correlation between bands even hundred bands separated away; while, on the other hand, some hyperspectral data cubes have a very weak average correlation values Fig. 4, Fig. 5. Inter band correlation matrices can be classified according to inter-band correlation; to have "Weak Spectral correlation matrix" (WSCM), or "Strong correlation Matrix" (SSCM); this can be measured according to mean correlation values indicated by spectral correlation matrix as in Fig. 2. Ten hyperspectral data samples are processes and used in this study; Table 1, illustrates the details of each data samples, associated figure that reflects the image view of spectral correlation matrix, and name of correlation matrix used in calculations.


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Fig. 1. Comparing SCM computed using wavelet transform on bands and

original ands, respectively, correlation 0.9137.

Fig. 1. Illustrates some statistical values about each data samples; that includes, mean value, variance, standard deviation, median, minimum, and maximum values. Mean values is calculated as average value for each raw then averaging these values to get one mean value for the entire matrix. Variance is the square value of the standard deviation; while median is median value of the median for each raw. Color mapping of the correlation values, is illustrated in Fig. 4; and as it is seen, red color means strong correlation with values around 0.8 or higher; passing through the color graduation until weak correlation represented by negative values with blue color.

IV. ANALYSIS OF SPECTRAL CROSS CORRELATION MATRICES

As results are statistically analyzed in Fig. 2; it seems that correlation matrices can be classified into two categories; the first category, that has strong correlation as visually seen, in image view of these matrices; at the same time, theses matrices have relatively large mean values, basically greater than 0.1(SSCM); second category, that has small correlation less than 0.1(WSCM).

Fig. 2. Statistical measurements of SCMs

Hence; spectral correlation matrix that has mean value greater than 0.1(SSCM), has a group of correlated bands even if these bands are far from each other. Based on this basic assumption, more analysis of each (SSCM) is performed to study how these "Group Of Bands" (GOB), if exists, are correlated. Any spectral correlation matrix is symmetric around its diagonal, which is the nature of calculation method as in Fig. 3. "corr_mtxl" and "corr_mtxer" Represent the SSCMs; with a deep look of each of them it can be noticed that for "corr_mtxer" there is a strong correlation between the groups of bands starting from approximately band number 10 till band number 55, and group of bands starting from approximately band number 180 till band number 220 (GOB (~10-55) and GOB (~180-220)).

Fig. 3. SCM with IBCS, symmetric matrix

This correlation appears in a square manner, dashed square in Fig. 7, Fig. 8, this is called "Inter Band Correlation Square" (IBCS); almost all correlated GOBs have IBCS pattern in spectral correlation matrix. IBCS itself is not symmetric around spectral correlation matrix diagonal; otherwise, it is inter-band correlation triangle (IBCT); but it has its analog on the other side of the matrix diagonal. Checking of the existence of the IBCS or IBCT, allows determining the correlation between bands in hyperspectral data cube, this helps in band reordering techniques used in compression of

TABLE 1 SUMMARY OF HYPERSPECTRAL DATA SAMPLES DETAILS, ITS

CORRESPONDING FIGURES OF CORRELATION MATRIX, AND NAME OF CORRELATION MATRIX FURTHER USED IN THIS CONTEXT

Hyperspectral data

sample Details Figure

number Spectral

correlation matrix name

"hawaii_sc01" AVIRIS instrument: 512 lines x 614 samples x 224 bands, instrument bit

depth = 12 bits

Fig. 7 "corr_mtxh"

"maine_sc10" AVIRIS instrument: 512 lines x 680 samples x 224 bands, instrument bit

depth = 12 bits

Fig. 9 "corr_mtxm"

"Aviris_sc0" AVIRIS instrument: 512 lines x 680 samples x 224 bands, instrument bit

depth = 16 bits.

Fig. 4 "corr_mtx0"


depth = 16 bits.

Fig. 5 "corr_mtx3"


depth = 16 bits

Fig. 5 "corr_mtxh10"


depth = 16 bits.

Fig. 6 "corr_mtx18"

"f960705t01" AVIRIS instrument: 512 lines x 680 samples x 224 bands, instrument bit

depth = 16 bits.

Fig. 6 "corr_mtx11"

"ErtaAle" Hyperion instrument: 3187 lines x 256 samples x 242 bands, instrument

bit depth = 12 bits.

Fig. 7 "corr_mtxer"

"LakeMonona" Hyperion instrument: 3176 lines x 256 samples x 242 bands, instrument


Fig. 8 "corr_mtxl"

"MtStHelens" Hyperion instrument: 3242 lines x 256 samples x 242 bands, instrument


Fig. 8 "corr_mtxhel"


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hyperspectral data [12], [13]; doing so, can be a very deterministic rule for band grouping and reordering strategy. Determining group of bands, that are highly correlated, is one of the interesting subjects [11], [12], [13] that would increases the efficiency of using compression coders, especially video codec [19], which depend on exploiting the maximum redundancy between frames, band in this case, to achieve higher compression ratio [13] [20], [21].

Fig. 4. Image view of SCM for "corr_mtx0" indicating the color mapping.

Fig. 5. Image view of SCM for "corr_mtx3", and "corr_mtx10",

respectively

Fig. 6. Image view of SCM for "corr_mtx18" and "corr_mtx11",

respectively

Fig. 7. Image view of SCM for "corr_mtxer" and "corr_mtxh", respectively

V. INTER-BAND CORRELATION SQUARE

Inter band correlation square is pattern of spectral correlation between bands in hyperspectral data; finding this square(s) refers to the location of the group(s) of bands that are highly correlated, and usually these GOBs are far away from each other. Edge detection is concept of image processing that helps to locate edges in the processed image; some algorithms are used in this area; such as, Sobel Method, Prewitt Method, Roberts Method, Laplacian of Gaussian Method, Zero-Cross Method, and Canny Method.

Fig. 8. Image view of SCM for "corr_mtxl" and "corr_mtxhel",

respectively

Fig. 9. Image view of SCM for "corr_mtxm"

The interest here to find the algorithm that determines the location(s) of the IBCS in the (S)SCM; the algorithm should, at least, be able to determine the location of the biggest IBCS; or, if many similar exists, to determine at least one of them. The Canny method finds edges by looking for local maxima of the gradient. The gradient is calculated using the derivative of a Gaussian filter. The method uses two thresholds, to detect strong and weak edges, and includes the weak edges in the output only if they are connected to strong edges. This method is therefore less likely than the others to be fooled by noise and more likely to detect true weak edges [22]. Comparative Study of these techniques [22] have been carried out; also performance analysis of each of them [24], recommends that Canny Method has better performance while detection of edges and less sensitivity for noise. Using "Canny method" to estimate the edges of the IBCS and IBCT; we got the results in Fig. 10 and Fig. 11.

Fig. 10. Canny Edge detection for WSCM

Fig. 11. Canny Edge detection for SSCM


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Finding the highest IBCS, requires an iterative process, beginning with highest threshold in the matrix; that corresponds to highest possible correlation values between bands, the iteration step resolution will invoke more iterations; it is recommended to examine the matrix strength, as indicated earlier, by its mean value, i.e. (SSCM or WSCM); most probably, WSCM will have no IBCS or if it has, it will be small. Fig. 12. Illustrates the process of finding the first (strongest IBCS) using canny method staring from threshold 0.95 and step of .05. For correlation matrix "corr_mtxhel"; It has shown that at threshold of 0.85; the strongest IBCS has occur, while further smaller threshold will give unwanted edges to the results; we should notice that the strongest IBCS has not the highest value in the matrix, since the regions near the diagonal should have higher values. If we tried the same iteration for WSCM, "corr_mtxm", we will have the result in Fig. 13; and as it is seen, we needed more iteration to find a small IBCS, which is also detected by incomplete square, further iterations behind this, resulted in the unwanted edges.

Fig. 12. Iterative process to find IBCS using "canny method" for SSCM

VI. BANDS REGROUPING TECHNIQUE

As illustrated in previous section, SCM can be strong or weak, strong SCM always has IBCS, and / or IBCT; these facts can be exploited in data compression techniques that employ prediction algorithms. Finding IBCS in SCM will help in determining groups of bands that are highly correlated to each other’s; detection threshold used in edge detection process of each IBCS/IBCT is the correlation value for each GOB, which indicates the level of similarity between bands and each other. We will take "corr_mtxer" as SSCM, to investigate the principle of grouping based on IBCS/T. for example, there is a strong correlation between the groups of bands starting from approximately band number 10 till band number 55, and group of bands starting from approximately band number 180 till band number 220 (GOB (~10-55) and GOB (~180-220)).Fig. 15, illustrates the process of finding IBCS/T in corr_mtxer SCM, starting from threshold of 0.7 down to 0.1. As a result GOBs that have strong correlation are stated in Table 1. We can see that GOBs are correlated to each other are separated away from each other, this link between GOBs are illustrated in Fig. 14. Regrouping of these bands based on SCM-IBCS/T; is the most efficient exploitation of inter-band spectral redundancy for hyperspectral data, as it gives a complete

picture of how bands are correlated to each other and how far each GOB from its closest GOB.

Fig. 13. Iterative process to find IBCS using "canny method" for WSCM

VII. CONCLUSION

In this paper, we have studied the spectral cross correlation structure of hyperspectral data cube for ten data samples; spectral cross correlation matrices have been constructed for each data sample; looking at the image view of these matrices; it was noticed that usually spectral correlation matrices can be classified into strong and weak correlation matrices, measured by matrix mean value; and for most of the spectral correlation matrices, there are group of bands correlated to another group of bands far away from each other; we identified the correlation region where groups of bands are correlated as inter band correlation square; canny method for edge detection has been found to be the best method to locate inter band correlation square in the correlation matrix. Determination of the highly correlated group of bands helps in band reordering and regrouping technique of the hyperspectral data that is mainly targets compression of hyperspectral images exploiting spectral redundancy. based on edges acquired from edge detection process; it was noticed that group of bands are correlated to some other group of bands, sometimes far away hundred(s) of bands from each other; this analysis of correlation matrix has introduced new procedure of getting a complete picture about the similarity of all bands with each other over the whole data cube; this techniques proposes a new method for regrouping hyperspectral bands based on correlation similarity measurement. Regrouping of these bands and linking each group to another group represents a good approach for prediction based hyperspectral compression.

Fig. 14 GOBs correlation with each other


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Fig. 15 -finding edges in corr_mtxer SCM, thresold from 0.7 down to 0.1

Table 1 Group of bands and correlation threshold value of detection Detection Thr. GOB GOB

0.7 9-53 9-53

0.65 81-120 9-53

0.6 181-221 101-120

0.45 181-221 81-96

0.4 125-165 9-53

0.3 181-221 9-53

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